We have generalized the approach to the problem of neutrino oscillation in an external magnetic field, developed in [1]}, for the case of three neutrino flavours. The obtained expressions can be reduced to those known before by setting \(\theta _{13} = \theta _{23} = 0\) . The effect of non-zero CP-phase is examined. It is shown that only \(P(\nu _e^L \rightarrow \nu _{\mu }^L)\)  and \(P(\nu _e^L \rightarrow \nu _{\tau }^L)\)  exhibit dependence on \(\delta \) . Using our approach, it is also possible to investigate the mass hierarchy effect on the phenomenon of neutrino oscillations in a magnetic field, but this is beyond the scope of the present paper. The obtained results are of interest in applications to neutrino oscillations under the influence of extreme astrophysical environments, for example peculiar to magnetars and supernovas, as well as in studying neutrino propagation in interstellar magnetic fields.
